Department of Mathematical Sciences
T. Khan
Associate Professor

Education
Teaching Interest
Research Interest
Publications
Files and Links

Contact Information:

Martin Hall O-201, Box 340975                          Tel: (864) 656-3257
Clemson University                                              Fax: (864) 656-5230
Clemson, SC 29634-0975                                    Email: khan@clemson.edu

Education:

Ph.D. University of Southern California, 2000
M.S. University of Southern California, 1996
A.B. Occidental College, 1994
H.S. Diploma Southwestern Academy, 1990

Teaching Interest:

Real analysis, complex analysis, functional analysis, mathematical methods for physics and engineering, linear algebra, numerical methods, Fourier analysis, partial differential equations, control theory, estimation of infinite dimensional systems, special topics in biomedical imaging, and biological information processing.

Research Interest:

Mathematical modeling, simulation, and analysis of statistical behavior of smart grid power system network, inverse problem or parameter estimation problem for partial differential equations or infinite dimensional systems, with particular emphasis on approximation and control with applications to biomedical imaging.

Selected Publications Link:

  1. Y. Epshteyn, T. Khan, and B. Riviere, "Inverse Problem in Optical Tomography using Discontinuous Galerkin Method," SIAM Journal of Scientific Computing, in review.
  2. A. Smirnova, R. Renaut, and T. Khan, "Convergence and application of a modified iteratively regularized Gauss-Newton algorithm," Inverse Problems, accepted.
  3. T. Khan and A. Thomas, "On some new integrals involving associated Legendre functions and some new integrals over the unit sphere," International Journal of Applied Mathematical Analysis and Applications, Vol 1/29-39 (2005).
  4. T. Khan, A. Thomas, and J. Yoon, "On Uniqueness in Refractive Index Optical Tomography," Inverse Problems, Vol 22/2, pp L1-L5 (2006).
  5. J. Peterson and T. Khan, "Abstract action potential models for toxin recognition," Journal of Theoretical Medicine/Computational and Mathematical Methods in Medicine, Vol 6/4, pp 199-234 (2005).
  6. T. Khan and A. Thomas, "Inverse Problem In Refractive Index Based Optical Tomography," Inverse Problems, Vol 22, pp 1121-1137 (2006).
  7. T. Khan and A. Thomas, "Comparison Of $P_N$ Or Spherical Harmonics Approximation For Scattering Media With Spatially Varying And Spatially Constant Refractive Indices," Optics Communications, Volume 255, Issue 1-3, pp 130-166 (2005).
  8. T. Khan and A. Thomas, "On derivation of the radiative transfer equation and its spherical harmonics approximation for scattering media with spatially varying refractive indices," Technical Report: TR-2004-12-KT, Department of Mathematical Sciences, Clemson University, Clemson, South Carolina, December (2004).
  9. A.B. Bakushinsky, T. Khan, and A. Smirnova, "Inverse Problem in Optical Tomography and its Numerical Investigation by Iteratively Regularized Methods," Journal of Inverse and Ill-posed Problems, Volume 13, Number 4, pp 1-14 (2005).
  10. T. Khan and P.M. Reppert, "A finite element formulation of frequency-dependent electro-osmosis," Journal of Colloid and Interface Science, Volume 290, Issue 2, pp 579-581 (2004).
  11. T. Khan and A. Smirnova, "1D Inverse Problem In Diffusion Based Optical Tomography Using Iteratively Regularized Gauss-Newton Algorithm," Applied Mathematics and Computation, Vol 161/1 pp 149-170 (2004).
  12. T. Khan and M. Pinsky, "On Some Integrals Over A Unit Sphere," Technical Report:TR-2003-5-TK, Department of Mathematical Sciences, Clemson University, Clemson, South Carolina, October (2003).
  13. T. Khan, "Inverse Problem In Optical Tomography Using Diffusion Approximation and Its Hopf-Cole Transformation," Journal of Systemics, Cybernetics, and Informatics, Volume 1, Number 6, October (2003).
  14. P.M. Reppert and T. Khan, "Porous Media Evaluation Using Frequency-Dependent Electrokinetics," Proceedings of the IUTAM Symposium on Mechanics of, Physicochemical and Electromechanical Interactions in Porous Media, Amsterdam, The Netherlands, May (2003).
  15. T. Khan and H. Jiang, "A New Diffusion Approximation To The Radiative Transfer Equation For A Scattering Media With A Spatially Varying Refractive Index," Journal of Pure and Applied Optics: A, Volume 5, Number 2, March (2003).
  16. T. Khan, "An overview of the ill-posed inverse problem in optical tomography," Technical Report: TR-2003-06-TK, Department of Mathematical Sciences, Clemson University, Clemson, South Carolina, July (2003).
  17. T. Khan, "Scaling/preconditioning in diffusion based optical tomography", Technical Report: TR-2003-06-TK, Department of Mathematical Sciences, Clemson University, Clemson, South Carolina, July (2003).
  18. Y. Xu, X. Gu, T. Khan, and H. Jiang, "Absorption And Scattering Image of Heterogenous Scattering Media Can Be Simultaneously Reconstructed Using DC Data," Applied Optics, Volume 41, Number 25, September (2002).
  19. N. Jalili, T. Khan, and S. Ramadurai, "On the Nonlinear Modeling and Identification of Piezoelectric Inertial Actuators", ASME International Mechanical Engineering Congress and Exposition, New York, November (2001).
  20. T. Khan, B. Yang, and C. Wang, "Control of Distributed Parameter Systems: Applications to Space Structures with Active Materials", 2000 American Control Conference Proceedings, Chicago, IL, June (2000).
  21. T. Khan, "Inverse Problems, Identification, and Control of Distributed Parameter Systems: Applications to Space Structures with Active Materials," Ph.D. Thesis, University of Southern California, Los Angeles, California, USA, May (2000).
  22. C. Wang, P. Chen, A. Madhukar, and T. Khan, "A Machine Condition Transfer Function Approach to Run-to-Run and Machine-to Machine reproducibility of III-VCompound Semiconductor Molecular Beam Epitaxy," IEEE Transactions on Semiconductor Manufacturing, 12-1, 66-75 (1999).
  23. T. Khan, B. Yang and C. Wang, "Modeling and Control of Space Structures with Active Materials," AIAA Guidance, Navigation and Control Conference and Exhibit, American Institute of Aeronautics and Astronautics, Portland, OR, August (1999).

Further Information:

Page Comments or corrections to: T. Khan
Last Updated June 30, 2001
http://people.clemson.edu/~khan